It is an older house. I have 3 separate black wires and a bundle of white wires tied together inside the box. It is supposed to control a patio light and a kitchen light on the 2 switches on the dual switch, but they either both turn on or both turn off.

Thank you.

You need to look at the back of the dual switch. One side is marked Line. There is also a small brass tab connecting the 2 line screws. This allows you to have 1 power lead and 2 out leads, or with the tab removed, 2 power leads and 2 out leads. Since you have 3 blacks, it appears you have 1 in and 2 out. Using a neon tester or VOM, find out which black lead is the power in. Connect that to the Line side. Connect the other 2 blacks to the 2 terminals on the other side of the switch. Whites stay bundled. Let us know how it works out.