Do two inserts. If your database supports it, do them in a transaction and/or a batch. If you think it's likely that the second one will fail, you might want to put it in a transaction so you can roll the first one back.
You will need to generate a key for the customer ID - this might be automatically done by your database, in which case you'll need to determine what it is so you can use it as a FK for the other table. None of this is difficult and it's all documented in your database's documentation*
Mark
*Unless you're using something really crap.