You wont find a paid hosting solution that will do "both" at the same time.OK - Apparently there are- I just could not find any for under 20USD a month.
I thought You will need to buy the PHP platform and .NET platform and code your site to use the best of both worlds - for the price of two.(somebody like streamline . net)
If you can get a VPS (virtual private server) will be cheaper and more configurable, create a windows(with IIS)[or WAMP] and Linux(Apache + PHP)[LAMP/XAMP]
But it is possible to run 1 platform only with the latter running as plugin.
Using that you can use .NET /PHP togheteher BUT -
on Linux the PHP is Long term support and .NET is an addon(not supported via LTS)
on Windows .NET is the base with PHP an addon(installable executable and works good- but not supported by Windows in any way)
So the support for the 'addon' is not long term and used at your own risk with updates being released for it much later than the base version.
if you can you make your own VPS server, and create your own Virtual Server completely stand alone on the same machine,with several virtual platforms using private ports internally to communicate with each other. Windows Server and Linux Distro and make them "talk" to each other in the way you like. Then a third could host the actual site and use whatever software you need form the other two VPS's
That would be supported by each respected vendor and you will always have the latest updates available directly on the platform.