I disagree, this doesn't work out fair if there's a big disparity in income, especially if the bills are high compared to income. The employed partner may well be able to pay 85% of the bills but STILL have way more spending money than the other partner, even if the non-employed partner is working just as hard looking after the children, doing housework etc.
For example - if total income for the month is £2000 but bills come to £1500, the employed partner, if earning/paying out 85% of those, would pay £1275 on bills but would still have £425 a month left to spend on themselves, or around £100/week. But the non-working partner, although "only" paying £225 on bills, would be left with just £75 of spending money for the whole month - less than £20 a week. (Plus if that is the only cash they have, they may well end up spending much of it on kids' activities, in my experience, as a lot of the mums-and-tots type activities want cash...).
So this is really unfair on the non-working parent and will over time make a huge difference to what they can do/have access to compared to their partner, and their ability to build up any savings. If you further increase the proportion of income spent on bills, that personal spending money ends up pretty much disappearing altogether for the non-working parent. (And remember that the working parent is also likely to be topping up their pension at the same time, so also adding to their savings for later life, while the other isn't getting any!)
So I'm with Changingplace - the only really fair way to do it (assuming the work being put in by both partners is reasonably equal, and with two under-3s and a part-time job, I'm sure it is at least equal!), is to pool all income and then get equal spending money each after bills/savings.