You would need to find a lender willing to loan you money. However, if you're behind on your mortgage you would not be a good credit risk. If you did find a lender willing to refinance it would...
In general, the majority of traditional mortgages require that both principal and interest (P&I) is paid on a monthly basis. There are Interest-Only products which are geared towards only paying...
You will make up the payments in the refinancing deal--check with your current mortgage company. Hopefully, you have some equity that will cover this and the cost of refinancing.