If you and your partner have both been working and had separate accounts, then becoming a housedad is going to be a shock. You're going to have to ask for house-keeping money. Worse than that, you're going to have to ask for pocket money. Consider a joint account. You're working as a family team and the money is jointly yours. This will, of course, require a certain level of communication to avoid going over-drawn, etc, but it will save you having to beg every time you need a new pair of socks.
Sad as it sounds, pocket money is still a good idea. You should both have some money each month to spend on whatever you want without having to justify it to the other. How much and what it covers is up to you and your budget. For instance, if my wife or I buy a DVD then it's from our own money but nights out (rare as they are) are from the main stash. My wife has her own account for pocket money and birthday money. I just keep a tally in my head. Whatever works.
All the details below are entirely out of date. DON'T RELY ON ANYTHING HERE. That said, I'm leaving it up because it will give you a taste of things to think about and an idea of the bureaucracy you'll have to deal with...
Having your own money to spend is important for self-esteem. If you live in the UK you have two possible sources of income from the government besides what you can blag from your partner:
First off, as the primary carer, make sure the child benefit is being paid to you. This protects your entitlement to a state pension and is important. Bear in mind that the benefits people won't believe you and will assume you've filled out the form wrong and try to give the money to your partner anyway. Don't let them.
This is a great scheme whereby your partner pays tax to the government and the government then gives it to you.
Basically you work out your expected gross (ie before tax) joint income for the current year and then subtract pension contributions, Gift Aid, maternity pay and non-taxable benefits. You then tell this amended income to the Inland Revenue, along with the number of hours you each work per week, how many children you have and their date of birth. They shove some entirely other information into their Arcane Calculating Machine of Disaster and then they send you the wrong amount of money. Luckily, they will send both you and your partner a four page letter documenting their mistakes. Then you phone them. They correct some of the mistakes, make others, change all your payments and then send both of you another four page letter. This continues for several months. They finally get it right but then your expected income changes and it all begins again.
The pain is worth it, though.