If you have more questions...you should contact the Dr. and ask them. You are paying for a service and your husband should know EXACTLY what his disharge instructions are so he can follow them carefully to heal.
Most compression fractures will heal within 8 weeks or so with rest, medication, and wearing the brace.
Did they not even tell you all to follow up with an Orthopedic surgeon in x amount of weeks/two months?
Carefully read every line that are in his discharge papers.
It's important to not twist, bend, lift things and to make sure he wears the brace for as long as is needed.
No one here is a medical professional so it's imperative to call the Dr. back to verify all of this.
Since surgery was not needed at the time of the accident...that is a good sign so hopefully it will heal and he will be good to go