SDLT is calculated on the value being transferred, so however you work out your partners share it will be less than the �150,000 threshold. A SDLT return still needs to be made.
If your partner is paying half the mortgage then the usual calculation would be to attribute the shares as a percentage or proportion including the one half of the mortgage. ie his interest would be 8000 + 45000 (53000) and your interest would be 87000 + 45000 (132000) with each of you suffering a deduction of one half of the value of the mortgage upon any sale. This does produce a potentially very different result from using just the equity, but in principle someone who contributes to the purchase by a mortage which they pay is considered to be in the same position as if they had contributed cash.
However the real answer to your question is that the shares will be calculated in the way that you and he agree at the outset to them being calculated. You can agree anything that seems fair to you, but the important thing is to get it all agreed and written down.