This is not a template. This is architecture, in particular three-level architecture . The levels you have
1) View
2) Data Processing (ASP / NET)
3) database
A design pattern is a code pattern to solve a common problem. For example, the Singleton pattern is a solution to the problem of ensuring that the application has only one instance of something.
Architecture is a general approach to developing an application as a whole. In your case, you have a web client, a processing layer, and a data layer.
Please note that depending on your design, client-side code may be considered as your own application, which may have its own architecture (for example, MVC architecture).
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