yes it is possible, but most times it is libraries that are used to write frameworks. Both are codes, but libraries and frameworks are very different. Like we once said somewhere on africoders, you call a library when you use it. But when dealing with frameworks, the frameworks call your code. This is why it is difficult to build a framework with another framework. It is better to write your framework yourself if need be, and this writing of framework yourself is not advisable unless you REALLY REALLY REALLY have a good reason to do this. It is mostly easier to study existing frameworks and use them to build your stuffs.
And supporting DHTML more, you better use framework as an abstraction for another system. CMS as an example, Drupal is a CMS and a framework. Drupal framework was used to develop drupal CMS. Another is Laravel being used for October CMS and likes.
You're literally saying I another words, building an OS with an OS. Instead building an OS from a kernel. Or building a Car with a Car, when you should say building a Car with collection of mechanical/electrical components