Sorry Mate. Not married, she is a nobody and not entitled to any benefits. You may be able to put her on your travel companion list.
If you do get married I am not sure about the child. You may have to adopt the child legally. I am not sure about this.
When you do have it set up, you are limited to a certain amount a day. You will most likely need extra medical insurance from somewhere in case your wife or child has an accident. You have a limit and it can be reached very quickly in Hong Kong. You as the employee may have a limit, but not sure.
I am sure some on this forum have extra insurance and could let you know.