Hope you had a great new year!
We do support such hosted pages using a combination of iframe and our APIs. Here's a document that can help you set up something similar to this: https://www.chargebee.com/tutorials/embedded-hosted-pages-example.html#
Please note that this is a reference implementation and might require tweaking to customize for your requirements.
Trust you are doing great!
We recently released a revamped version of our hosted pages, Checkout V3 that support hosted pages and customer portal served through a modal popup. This requires you to use our drop-in script on your side. Here are the implementation docs for it.
This is a bit more stable and easier than the previous solution. Do try it out and let me know if you have any questions.