from OnGUI (using normal rect positions for button):

if (Event.current.type == EventType.MouseUp && yourInvisibleButtonRect.Contains(Event.current.mousePosition))
{
    //jump
}

from Update (the rect needs to be defined with bottom left of the screen at 0,0):

if (Input.GetMouseButtonDown(0) && yourInvisibleButtonRect.Contains(Input.mousePosition))
{
    //jump
}

Create a GUIskin or GUIStyle with the texture of the Button as a fully transparent. The button will be invisible but will retain all normal Button functionality.