dm101,
I hate to be the bearer of bad news, but it is irrelevant what the bank calls your mortgage, investment or whatever, as far as revenue would be concerned.
A mortgage for your principle private residence would not be considered to be a mortgage for an investment property(in the eyes of revenue) and therefore you can't offset the mortgage interest against the rental income.
You are entitled to tax relief on the mortgage as it is for your principle private residence and this is normally done at source by the bank. You are allowed an income of around €7,000 rental income(tax free) through the rent a room scheme, but I'm not sure what happens if your income exceeds that. Others may be able to advise.
I'm not an expert, but I'd be confident that my understanding is correct.