How are RSA and ElGamal compatible in PGP?
When creating a signed and encrypted PGP message, you only use your own keypair in the signing phase -- it's not used when encrypting the message (that only uses the recipient's public key). The recipient uses their own keypair only to decrypt the message, not to verify the signature. The two keypairs don't interact at all; that's why they don't have to be the same algorithm.