Looks like this one[1] or this[2] can do this for you. I can't vouch for them though.

Why not accept BTC directly instead of routing it through credit card?

[1] https://plasmapay.com/business
[2] https://coingate.com/accept-bitcoin

I am not aware of such as payment getaway who accept bitcoin & visa/master card together. If there is any you will encounter high fee, even some fiat getaway charge 2%. So I think it would be better for you just use separate payments getaway for fiat and crypto currency. So that you would minimize your extra fee. For cryptocurrency I will suggest to use BTCPAY server. There is getaway for multiple crypto currency. Most important thing is fund will be full control by you if you use your own host. Even you may accept bitcoin via lighting network. There is also third party host available if you are not much experience and you don't want to host by yourself. There is some pros and cons so read before attempt to use. You don't need to spend extra fees or whatever. For fiat find some other getaway, I am not familiar with it so I can't suggest any getaway. Please always try to avoid third party getaway especially for cryptocurrency if your business value is high.

Probably Bitpay can help! Get in touch with their support team to know more about their offerings. Bitpay is one of the most oldest and trusted settlement provider in this market for cryptocurrency. If you have a good volume, they may be able to offer some customized solution as well. It's better for you to get in touch with them to see if they will send your bitcoin payment instead of fiat. They are mostly used for crypto to fiat settlement for the merchants. But exception can be made I guess!

Bitpay I believe is a crypto processor and I am not looking to purchase BTC.