How can I match/align two objects along 1 axis only?

As I read through your question, I can interpret what you want in a few different ways. Some simpler, some harder. I'm going to pick a middle of the road solution. It allow for the base box to be at any arbitrary angle on the 'Y', but assumes that it is level with respect to the XZ plane. It also assumes that you might be rotating the character at the same time you are bringing the characters in line.

The solution is to find the closest point on the Vector3.right of the base box to a character. Then the script brings that point up on the 'Y' to the level of the character. This point is then used for a Lerp(). I also added bringing the character into rotational alignment.

Put the following script on each character. Then you need to drag and drop the base cube onto the 'baseBox' variable for each character. Or you could do a simple rewrite and have this script find the base cube using GameObject.Find().

 #pragma strict
 
 var baseBox : Transform;
 var speed = 2.0;
 var rotSpeed = 1.0;
 
 function Update() {
 
     // Find the closest point on the transform.right of the base box
     var v3 = transform.position - baseBox.position;
     var t = Vector3.Dot(v3, baseBox.right);
     var pt = baseBox.position + baseBox.right * t;
     
     // Bring the point up to the level of this game object
     pt.y = transform.position.y;
     
     transform.position = Vector3.Lerp(transform.position, pt, speed * Time.deltaTime);
     
     // Rotation
     var q = Quaternion.LookRotation(baseBox.right);
     transform.rotation = Quaternion.Slerp(transform.rotation, q, rotSpeed * Time.deltaTime);
 }