I assume that you're talking about a Pay-to-pubkeyhash (P2PKH) transaction, which is the most common transaction on the network at this time.

The pubkey script of a P2PKH transaction output contains the hash of the public key (what you call HASH160).

pubkey script:  OP_DUP OP_HASH160 <PubkeyHash> OP_EQUALVERIFY OP_CHECKSIG

Said PubkeyHash can be converted into the address by prepending two zeroes expressing it in base58check, a more human readable format.

I assume that you're talking about a Pay-to-pubkeyhash (P2PKH) transaction, which is the most common transaction type on the network at this time.

The pubkey script of a P2PKH transaction output contains the hash of the public key (what you call HASH160): 
OP_DUP OP_HASH160 <PubkeyHash> OP_EQUALVERIFY OP_CHECKSIG

Said PubkeyHash can be converted into the address by prepending two zeroes and expressing it in base58check, a more human readable format.