I would suggest using Mac Drive by Mediafour: http://www.mediafour.com/products/macdrive
I've used their product for years and it has always been rock solid. I'd say at $49.99, it is reasonably priced too. And honestly, you may find a free solution, but to me, data integrity will always trump a slight to the wallet.
That is if you absolutely want one partition, but considering that one is a dedicated Time Machine repository, I would advise against it. While Time Machine makes a simple folder with all the backups (Backups.backupdb), it is ill-advised to store anything else on that particular partition. I know people that do it without problems, and all Apple says about the practice is the following:
Note: Time Machine works best if you use your backup disk only for
Time Machine backups. If you keep files on your backup disk, Time
Machine won’t back up those files, and the space available for Time
Machine backups will be reduced.
But again, it's just good to keep things separate in my opinion. I'm not one for arbitrary compartmentalization, but in the case of backups, maybe letting them have their own room might not be such a bad thing.