Rigidbody Jumping for Character Controller

I just finished my character controller except for the fact it can't jump. When I have tried to make it jump with CharacterController.move, it teleports upward then slowly falls down. I would like to make my game have realistic physics all around, so I thought I should make a gameObject with a rigidbody that does all the gravity based physics. My hierarchy has an empty Player GameObject with a PlayerModel GameObject(Controlls movement and has controller on it), PlayerCamera, and a PlayerRigidbody that is an empty game object with a rigidbody attached to it. I would like to know the best way to move my rigidbody with the player and then let my player be affected by the way the rigidbody moves on the y-axis. Here is my code PlayerController:

 using UnityEngine;
 using System.Collections;
 
 public class PlayerController : MonoBehaviour {
     
     private CharacterController player;
     public float forwardMult = 1;
     public float backwardMult = 1;
     public float sidewaysMult = 1;
     public float gravity = -2;
     public float jumpHeight = 10;
 
     SmoothMouseLook smoothMouseLook;
     float jump = 0;
     Rigidbody rb;
     Camera firstCam;
     GameObject parent;
 
     void Start () {
         parent = transform.parent.gameObject;
         player = gameObject.GetComponent<CharacterController> ();
         rb = parent.GetComponentInChildren<Rigidbody> ();
         firstCam = parent.GetComponentInChildren<Camera> ();
     }
     
     void FixedUpdate () {
 
         float moveVertical = Input.GetAxis ("Vertical");
         float moveHorizontal = Input.GetAxis ("Horizontal");
 
         //Applies forward/backward multipliers
         if (moveVertical > 0) {
             moveVertical *= forwardMult;
         }else if (moveVertical < 0){
             moveVertical *= backwardMult;
         }
 
         //Moves the Camera & Rigidbody
         firstCam.transform.position = new Vector3(transform.position.x, transform.position.y + 1, transform.position.z);
 
 
         //Adds Camera Rotation
         Vector3 tempRot = new Vector3 (0.0f, firstCam.transform.eulerAngles.y, 0.0f);
         transform.eulerAngles = tempRot;
 
         //Defines player movement
         Vector3 verticalMovement = transform.forward * moveVertical * Time.deltaTime;
         Vector3 horizontalMovement = transform.right * moveHorizontal * Time.deltaTime * sidewaysMult;
 
         //Jumps
 
         //Moves Player
         player.Move (verticalMovement + horizontalMovement);
         player.Move (new Vector3(0.0f, gravity, 0.0f));
     }
 
 
 }
 

SmoothMouseLook:

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 
 [AddComponentMenu("Camera-Control/Smooth Mouse Look")]
 public class SmoothMouseLook : MonoBehaviour {
     
     public enum RotationAxes { MouseXAndY = 0, MouseX = 1, MouseY = 2 }
     public RotationAxes axes = RotationAxes.MouseXAndY;
     public float sensitivityX = 15F;
     public float sensitivityY = 15F;
     
     public float minimumX = -360F;
     public float maximumX = 360F;
     
     public float minimumY = -60F;
     public float maximumY = 60F;
     
     float rotationX = 0F;
     float rotationY = 0F;
     
     private List<float> rotArrayX = new List<float>();
     float rotAverageX = 0F;    
     
     private List<float> rotArrayY = new List<float>();
     float rotAverageY = 0F;
     
     public float frameCounter = 20;
     
     Quaternion originalRotation;
     
     void Update ()
     {
         if (axes == RotationAxes.MouseXAndY)
         {            
             rotAverageY = 0f;
             rotAverageX = 0f;
             
             rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
             rotationX += Input.GetAxis("Mouse X") * sensitivityX;
             
             rotArrayY.Add(rotationY);
             rotArrayX.Add(rotationX);
             
             if (rotArrayY.Count >= frameCounter) {
                 rotArrayY.RemoveAt(0);
             }
             if (rotArrayX.Count >= frameCounter) {
                 rotArrayX.RemoveAt(0);
             }
             
             for(int j = 0; j < rotArrayY.Count; j++) {
                 rotAverageY += rotArrayY[j];
             }
             for(int i = 0; i < rotArrayX.Count; i++) {
                 rotAverageX += rotArrayX[i];
             }
             
             rotAverageY /= rotArrayY.Count;
             rotAverageX /= rotArrayX.Count;
             
             rotAverageY = ClampAngle (rotAverageY, minimumY, maximumY);
             rotAverageX = ClampAngle (rotAverageX, minimumX, maximumX);
             
             Quaternion yQuaternion = Quaternion.AngleAxis (rotAverageY, Vector3.left);
             Quaternion xQuaternion = Quaternion.AngleAxis (rotAverageX, Vector3.up);
             
             transform.localRotation = originalRotation * xQuaternion * yQuaternion;
         }
         else if (axes == RotationAxes.MouseX)
         {            
             rotAverageX = 0f;
             
             rotationX += Input.GetAxis("Mouse X") * sensitivityX;
             
             rotArrayX.Add(rotationX);
             
             if (rotArrayX.Count >= frameCounter) {
                 rotArrayX.RemoveAt(0);
             }
             for(int i = 0; i < rotArrayX.Count; i++) {
                 rotAverageX += rotArrayX[i];
             }
             rotAverageX /= rotArrayX.Count;
             
             rotAverageX = ClampAngle (rotAverageX, minimumX, maximumX);
             
             Quaternion xQuaternion = Quaternion.AngleAxis (rotAverageX, Vector3.up);
             transform.localRotation = originalRotation * xQuaternion;            
         }
         else
         {            
             rotAverageY = 0f;
             
             rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
             
             rotArrayY.Add(rotationY);
             
             if (rotArrayY.Count >= frameCounter) {
                 rotArrayY.RemoveAt(0);
             }
             for(int j = 0; j < rotArrayY.Count; j++) {
                 rotAverageY += rotArrayY[j];
             }
             rotAverageY /= rotArrayY.Count;
             
             rotAverageY = ClampAngle (rotAverageY, minimumY, maximumY);
             
             Quaternion yQuaternion = Quaternion.AngleAxis (rotAverageY, Vector3.left);
             transform.localRotation = originalRotation * yQuaternion;
         }
     }
     
     void Start ()
     {            
         if (GetComponent<Rigidbody>())
             GetComponent<Rigidbody>().freezeRotation = true;
         originalRotation = transform.localRotation;
     }
     
     public static float ClampAngle (float angle, float min, float max)
     {
         angle = angle % 360;
         if ((angle >= -360F) && (angle <= 360F)) {
             if (angle < -360F) {
                 angle += 360F;
             }
             if (angle > 360F) {
                 angle -= 360F;
             }            
         }
         return Mathf.Clamp (angle, min, max);
     }
 }

Any help is appreciated.