Chrome browser http links on a secure page taking to https domain

We have recently secured a web application with certificates so as to use https. Let us call this WebApp-A. This WebApp-A runs on port 8081. There is another server running at port 8744 on the same box which does not use https. Let us call this WebApp-B. A page on WebApp-A has links to pages on WebApp-B. The links that point to WebApp-B on WebApp-A page start with http and not https as expected. Note that domain for the both are same except the port number. Now the problem we are facing is, when a user clicks on a WebApp-B link on the WebApp-A page, which uses https, it takes to a https url for WebApp-B too, despite source showing the url to start with http. This behavior is seen on Chrome and Firefox, but not on IE. The behavior is inconsistent too. Sometimes it takes to https and sometimes to http. Things work when the URL goes to http but not when it goes to https. Can someone explain this inconsistency?