How do you drill a homemade double sided pcb
Your drill is probably not sharp enough. It is hard to keep an ordinary HSS (High-Speed Steel) twist drill bit sharp when drilling fiberglass.  That is why special carbide drill bits are typically used for drilling PCBs.  Another possibility is that you might be trying to drill too fast, pushing your way through before the drill has a chance to actually CUT the copper on the far side.

You can find many sources for special carbide PC board drill bits on Ebay by searching for: carbide pcb drill bits

It is prudent to buy them by the dozen because carbide is quite brittle and unforgiving of abuse.  And for the same reason, you should only use them in a drill press (or equivalent)  Never with a hand-held tool.

Another sources of carbide drill bits is ...
 - http://www.goldmine-elec-products.com/products.asp?dept=1273