Even with as many answers as already exist here, there's one option that hasn't been explained.
Don't change anything
#Don't change anything SinceSince your husband is getting paid more than before (as explained in the comments), you really should be getting more in your bank over time. Since you state that you can already easily pay your bills, you just have to let his paychecks accumulate before paying the bills.
Here's some math that might help, hopefully:
Random yearly salary: $120,000 (for easy math)
Monthly pay (ignoring taxes): $10,000
Bi-Monthly paycheck (again ignoring taxes): $5000
Equivalent Weekly paycheck (once again ignoring taxes): $2307.69 (52 weeks)
New weekly paycheck (ignoring taxes and including pay increase): $2500 (for easy math)
Each month, your husband used to get 2 paychecks that equaled $10k, now he generally gets 4 paychecks that equal the same amount. You don't have to do anything except wait to pay the bills at your normal time. If you have enough money in the bank already, you don't have to worry if it seems like more is going out than coming in, because that's just not true.
What is true is that for 4 months each year, you'll be getting an "extra" 5th check per month, which earns you $10k more a year, for a new salary of $130,000. You're already getting the same amount per 4 week month as before, so your finances are fulfilled, and with the raise, you're doing even better.
Of course, this example has been greatly simplified, but it should still show you how your new situation works with even as little as an 8% pay raise.
Budget
#Budget ItIt seems as if you have a basic budget: money comes in, so you pay the bills. That's great, but it's missing a gap in your peace of mind. No, I didn't spell that incorrectly. Since you are confused, possibly slightly panicking, and don't understand your new situation, you aren't seeing where your money is at clearly enough to leave your mind at peace with the new situation.
I could go on about different methods of budgeting and how they help & hinder, as well as what's right in your situation, but I won't. Instead, I'll point you to a great book that does it for me, in simple terms & concepts, which make it really easy to understand and implement. The book "America's Cheapest Family" has a variety of options for budgets and, as a side benefit, shows you how to maximize the benefit of how you spend your money while spending less of your money.
I'm not affiliated in any way with this book (any referral added to the link is done by SE, as they've done on previous Answers of mine), but rather I'm a satisfied customer. I've read the book at least twice and have learned better ways to manage my money and my budget.
This family has not only learned how to budget for themselves, but they've personally helped many people fix their own situations and wrote the book so they could help more people than those they can fit around their kitchen table. Also, the book really is written by the whole family. Most of it is tag-team written by the husband and wife, but the kids also chime in at different places in the book. The parents have taken the time to teach their kids how to budget, so the kids won't have the same problems the parents did.