Yes both languages will run without interference. In fact Applied Innovations supports, PHP, PERL, ASP and ASP.net at this time.
Content retrieved from: https://support.appliedi.net/kb/a382/can-i-run-both-asp-and-asp_net.aspx.
Content retrieved from: https://support.appliedi.net/kb/a382/can-i-run-both-asp-and-asp_net.aspx.