Adding jumps to grid movement character controller

Hey guys- I have a character controller I built which only moves along the grid in Unity.

It works great, but I can't seem to figure out how to get my character to jump and fall (in Y Axis) correctly. Does anyone have any recommendations for how I can achieve this?

Code (CSharp):

1.    
2. private float unitLength = 2;
3.  
4.     private void FixedUpdate()
5.     {
6.         Move();
7.     }
8.  
9.     void Move()
10.     {
11.         if (!Player.isDead && Player.gameStarted)
12.         {
13.             if ((increment < 1) && isMoving) { increment += speed / 1000; }
14.             else { isMoving = false; }
15.  
16.             if (!isMoving || currentDirection == Vector3.zero)
17.             {
18.                 //Check if next direction is valid. If so, set to current direction
19.                 if (CheckDirection(nextDirection))
20.                 {
21.                     currentDirection = nextDirection;
22.                     RotatePlayer(currentDirection);
23.                 }
24.  
25.                 //Check if current direction valid, set up movement for that direction and rotate player. Otherwise, stop (do nothing)
26.                 if (CheckDirection(currentDirection))
27.                 {
28.                     increment = 0;
29.                     isMoving = true;
30.                     startPoint = transform.position;
31.                     endPoint = transform.position + currentDirection;
32.                 }
33.                 else
34.                 {
35.                     RotatePlayer(nextDirection);
36.                 }
37.             }
38.             else
39.             {
40.                 transform.position = Vector3.Lerp(startPoint, endPoint, increment);
41.             }
42.         }
43.     }
44.  
45.  
46.     public bool CheckDirection(Vector3 direction)
47.     {
48.         Vector3 targetPoint = transform.position + direction;
49.         RaycastHit hit;
50.         if(Physics.Linecast(transform.position, targetPoint, out hit))
51.         {
52.             Debug.DrawRay(transform.position, direction, Color.red);
53.             if(hit.collider.tag == "Wall")
54.             {
55.                 return false;
56.             }
57.         }
58.         return true;
59.     }
60.