So if I understand you correctly, there is only the 3 wire, black, red, and white, in each light. And the black and white of the light splices onto the black and white of the 3 wire. I suppose that is why you are asking, because you have discovered that this does not work.
Since the 3 way needs to have two dedicated wires connect directly between both 3 way switches, and each light needs the white as a neutral, there is one wire missing. With the feed at one 3 way, the switched leg needs to come from the other 3 way switch.
Another 2 wire cable needs to come from the other 3 way and go to each light. If this cannot be done because the ceiling and walls are finished, thenthere are not many options.
You may look into remote control devices, called X-10 devices, or technology. With these you can get a transmitter switch that only needs a feed, and sends a signal back out on the feed, whcih will find it's way to the lights, where a receiver module at each light will see the signal and turn on the light.
These devices can be seen at: http://www.leviton-lin.com/catalog/C...talogSection=B
Searching the net for X-10 will find many other websites that offer these devices.