The @DMGregory's comment is what I was looking for.
I just take the character colliders and run for each one of them the call:
foreach(var characterPartCollider in characterPartsColliders)
This makes the character fall down through a platform. Then when I detect a collision with ...
Solved it by checking if the button is up AND the y velocity is more than zero. Basically the velocity code will not be executed when the character is falling. Here is the code snippet:
if (Input.GetButtonUp("Jump") && rb.velocity.y > 0)
isJumping = false;
rb.velocity = new Vector2(rb.velocity.x, 0f);