U.S Interbank Market Rate (other than the overnight cash rate)

Hi All,

Does anyone know how U.S Financial Institutions borrow from one another for a maturity that is longer than an overnight loan (as I realise the cash rate is the overnight rate)?
I’m interested in knowing whether there is a short term rate (for loans lasting longer than overnight eg. a month or 2) that U.S banks charge each other.
Australia has the 90 Day Bank Bill Swap Rate which Australian Banks use to borrow/loan short term funds to one another for maturities lasting longer than 1 day. I’d like to know whether the U.S has something similar which can be tracked to gain insight into the banking institutions expectations for future cash rate changes.

Cheers,
Lynchaldinho