We have a backup of sewage into the downstairs toilet and tub

What is your question?

I used to live in a townhouse complex and we were at the end of the line of homes. If someone flushed something down the line further down, every one of us up the line would get a backup from all the water from showers, dishwashing, and yes toilet crap.

There are many reasons for a backup, but the bottom line is, the sewage pipe is blocked somewhere. If you rent, call the landlord and he will get a plumber out to fix it. If you own your own home, again call a plumber, they will snake the line and remove whatever is clogging it.

We have a backup of sewage into the downstairs toliet and tub

This must be snaked out from the Downstairs lavatory roof vent. You will need to rent a sewer machine,(see image) to do this.
Go up on the roof and put out enough snake to reach the base of the stack and 20 feet more to reach the main. Good luck, Tom

... Or, remove downstairs toilet, use 3/4" snake cable and snake it through closet ring. This way, you accomplish lot more.

You may also have a cleanout within 18 inches inside or outside of the house. If not I would go with milos advice, pull basement toilet and auger that sucker all the way to your city main or private septic tank. If your roof isn't pitched to steeply, and you fill comfortable hauling a large machine up a ladder, then feel free to use the roof vent. Good luck and please let us know how it all works out.