You can use:
multichain-cli getblock <block_hash_here>
This will return a JSON containing the height of the blockhash. So you can find the previous:
multichain-cli getblock <height-1 here>
I hope I understood correct the question :)
Just tested it. Using getblock <blockhash> you get the JSON response in which you can find in the end of the response a key named: "previousblockhash"
So using getblock <value_of_previousblockhash> you can get the info you need.