The cost basis = the purchase price + improvements ... it has nothing to do with the debt or mortgages or refinancing.
When you refinance you are just taking out equity ( a nontaxable event) or lowering payments ... neither of which effects the underlying cost basis.
So when the program asks for the cost basis on a new asset placed in service just enter one amount. If you add the AC after you started depreciating the home THEN it would be entered as a separate asset.
Now some folks go crazy when placing a new property into service and breakout everything they can like all the appliances and make a dozen different entries but that is not needed at all and a big waste of time especially for your use ... so just make one entry for the home and call it quits.
