No this is not right. You should not be paying half the bills. If he is earning more than you, ALL bills and everything else should be proportional to your incomes.
Have a joint account that you both pay into proportional to your incomes. Then EVERYTHING for the house or the relationship comes out of it, including groceries, meals out together, jointly-agreed holidays, the lot.
Except for: your own cars, clothing, make-up, 'special' toiletries, personal hobbies, personal items such as a coffee or book you buy yourself, presents you buy for your family if they are not to be 'from both of you', and similar things.
However this only works if you can trust him not to take the piss and e.g. put load of his clothing and personal stuff in with a joint supermarket shop.
The mortgage is up for negotiation as it depends who owns the house and under what legal terms.
Then if he still has more money than you after his proportional contribution to the joint, he can decide if he wants to do things like pay for an 'upgrade' to afford a better holiday, or treat you to a meal that he pays for, or pay your car repair bill.
Or he could just be tight and save it all - but that won't matter as pretty much every joint expense you need or reasonably want is paid from the joint account.