Rain shouldn't affect the DSL internet signal if everything is sealed up correctly and no wires are exposed to the rain.
However sometimes yes the rain can affect a DSL signal if the connections are not sealed properly and moisture from the rain is getting into your telephone box outside on your house which can overtime corrode the copper wire connections.
The corrosion can then make your DSL internet signal drop out when it rains so you should have your ISP come out and check the connections to make sure they're not corroded.
The problem could also be out in the telephone companies box in the street or on the pole depending on whether your telephone lines are buried or are above ground.
If nothing is corroded and your wires are tightly connected and sealed off properly then the rain should not cause any problems with the DSL signal.