Interface for server requests and responses
You have to keep in mind that the earlier version of the .NET framework suffered in applying the interface segregation principle. In this case, the HTTP context includes methods associated with the request (ex. URL), the response (ex. HTTP status) and server utility functions (ex. map path).

With that in mind, the interface looks OK and familiar in terms of usage in comparison to the original HttpContext (System.Web) and HttpContextBase (System.Web.Mvc) and should be fine.

One aspect in regards to MVC that is hard to manage is the multiple data sources (query parameters, URL parameters, HTTP post Form values, routing parameters, session and the per request key/value store (HttpContext.Current.Items)) - perhaps it would be worthwhile to create an intermediary to manage these.