I was able to file an 1120S last year, I thought with the same software.
In order to file non-individual/business forms (1120C, 1120S, 1065, etc.) you would need TurboTax Business, not TurboTax Home and Business.
You would need separate software, one for your individual return, one for your business return.
Download link (business): TurboTax Business
Download link (individual): TurboTax Desktop Download Page