Someone may have dropped a 3 wire into the box from the last fixture or from a junction box in the ceiling. The switch sounds like a duplex top/bottom switch.
The power most likely comes in on the white and returns on the red and the black. GET A METER. Check it out. If you can't get a meter, turn the breaker off, connect the black and white. Turn the breaker back on and go look to see which light comes on. turn the breaker back off and connect the white and red, breaker back on, check again which light comes on. If nothing, turn the breaker back off, then try black to red. One of those wires will work with both lights and that will be your common power source. Pigtail it with 2 leads. Run one to each switch. Then the other 2 wires, one to each switch.