If you're the resident parent, he would pay you. The CMS calculation starts from his gross income only; your salary doesn't come into it. It's then reduced by the number of nights the children stay with him each year: If care is shared equally, nothing is payable. As you both work full time, he may well ask for 50/50, so bear that in mind.
School fees sit outside CMS. You can agree between you how they're paid, and the agreement can go into your financial consent order so it's enforceable. Cover the detail: proportions, extras like trips and uniform, and whether it runs through sixth form.
The starting point is an equal split of everything built up during the marriage, including pensions. The court can move away from 50/50 if one person's needs wouldn't be met. The key figures will be each of your mortgage capacities. At £50k he might borrow around four to four and a half times his income; you can borrow much more, although lenders will take the school fees into account. If his borrowing plus half the pot houses him somewhere suitable for the children to stay, equal may well stand. If it doesn't, your greater ability to meet your own needs from income is the argument for him receiving more than half.
Maintenance to him is possible, because of the income gap. But on £50k with a share of the capital, his needs may be met without it, and the courts prefer a clean break where they can. If there was a shortfall, it's more likely to be dealt with through a short-term order or an extra lump sum than open-ended payments.
Things that will change the picture are how much equity there is, both your pensions (yours is likely to be much larger), how many children and their ages, and how long you've been married.
Get a mortgage capacity letter from a broker for each of you, get your pensions valued, and pull together full figures on everything. Mediation is worth trying. It starts with a meeting on your own with a mediator (called a MIAM), who explains how it works and checks it's suitable, before any joint sessions with your husband. It doesn't sound like they will but if talks break down and you end up going to court, you'll have to have attended a MIAM before you can apply anyway.