Coach Battery Replacement Help

I think I have "Googled" myself into confusion! I have a 2000 Four Winds Infinity (35') that I bought used in 2009. I had one of my three 12V coach batteries to go bad (boiled, gurgled, leaked, smelled). I am planning on replacing all 3. The three batteries are all Interstate Workaholic 31-MHD's, which I do not think are Deep Cycle Batteries, and not sure they are the proper type batteries for coach use. The chassis battery is a deep cycle--which confuses me also. All the batteries are the ones that were installed when I purchased the RV. I was going to replace the Interstates with similar replacements; however, if they are not deep cycle, I do not know that is a good idea. I have also considered the AGM, but I have read some posts where the AGM's could create a problem with the RV's converter. Right now, I am just interested in replacing the coach batteries with the proper type, without having to worry about doing anything with the converter. Any comments and/or suggestions to alleviate my present confusion is greatly appreciated!