Is there an Android video chat client that displays video stream and text messages at the same time? I'm looking for a video chat app for Android, but I'm unable to find one that can display the video stream and text messages at the same time, it's either one or the other.
I tried for example Google Hangouts and Skype and both have this problem.
Screen estate should not be problem since it would be used on a tabled with external keyboard

Is there another app in the market that allows this? If possible I would like also to be able to call Windows clients.
Voice chat programs uses an Internet data stream.  It isn't up to the developer of the application.  No matter which app you find it will be limited based on your phone service provider and the type of phone you have.

Take a look at this (the protocols that are available via some services and phone types:

(taken from this thread, Can I talk and use Internet or other apps at the same time)


  If you really want to know why and how this happens, without all the
  techie speak - - - - 
  
  Verizon's 3G data and voice network is CDMA, and only a device with
  SVDO technology can use voice and data at the same time (as opposed to
  the current standard EVDO) on CDMA. The first device to do this was
  the HTC Thunderbolt. The Galaxy S3 also has SVDO, so you can surf and
  talk at the same time if you have Verizon 3G service. 
  
  The VZW iPhone does not have SVDO, so it can't do it. The iPhone on
  ATT and Tmobile can do this, as those two carriers don't use CDMA -
  they use GSM, which can do voice and data already. I don't know why
  specifically, but just know that Tmo and ATT are GSM and Sprint and
  VZW are CDMA. 
  
  Finally, any 4G LTE enabled phone on verizon can do talk and data at
  the same time, as the data will run over the LTE network and the voice
  runs over CDMA. So, devices like the Moto Droid Razr and other LTE
  phones can do talk and data at the same time, but only if LTE service
  is available. If in a 3G-only area, the Droid Razr can't do talk and
  surf together. 
  
  Make sense?


So if this is a needed feature you would have to shop for a specific phone provider and a specific phone that will allow you to use Data service and Phone service simultaneously... again, limited by the phone service and phone, not the app.