Is it possible to use Django and Node.Js?

It's absolutely possible (and sometimes extremely useful) to run multiple back-ends for different purposes. However it opens up a few cans of worms, depending on what kind of rigour your system is expected to have, who's in your team, etc:

• State. You'll want session state to be shared between different app servers. The easiest way to do this is to store external session state in a framework-agnostic way. I'd suggest JSON objects in a key/value store and you'll probably benefit from JSON schema.
• Domains/routing. You'll need your login cookie to be available to both app servers, which means either a single domain routed by Apache/Nginx or separate subdomains routed via DNS. I'd suggest separate subdomains for the following reason
• Websockets. I may be out of date, but to my knowledge neither Apache nor Nginx support proxying of websockets, which means if you want to use that you'll sacrifice the flexibility of using an http server as a app proxy and instead expose Node directly via a subdomain.
• Non-specified requirements. Things like monitoring, logging, error notification, build systems, testing, continuous integration/deployment, documentation, etc. all need to be extended to support a new type of component
• Skills. You'll have to pay in time or money for the skill-sets required to manage a more complex application architecture

So, my advice would be to think very carefully about whether you need this. There can be a lot of time and thought involved.

Update: There are actually companies springing around who specialise in adding real-time to existing sites. I'm not going to name any names, but if you look for 'real-time' on the add-on marketplace for hosting platforms (e.g. Heroku) then you'll find them.

Update 2: Nginx now has support for Websockets

You can't merge them. You can send messages from Django to Node.Js through some queue system like Reddis.