It isn't obvious to me how these two systems would interact. The head has a water hose to fill the tank and a waste hose to empty the tank. They're two systems I believe physically separate.
First of all, the toilet and the holding tank aren't two systems, they're two of the components in a single system--the sanitation system.
Every tank--water, fuel and waste-- has a hose to fill it and a hose and pump to empty it...and must also have a vent line. Tank vents have two main functions: to provide an escape for air in the tank that's displaced by incoming contents and a source of air to replace contents as they're drawn out.
If a blocked vent prevents air in the tank from escaping as the tank fills, the tank--the whole system--becomes pressurized...this creates back pressure that prevents anything more from going into the tank. In the sanitation system, that back pressure not only prevents bowl contents from getting to the tank, it pushes them back into the toilet. A toilet that's becoming harder to pump and/or "burps" and backs up is usually the first clue that the tank vent is blocked. Opening the deck pumpout cap releases the pressure...people who see the geyser usually find it very entertaining...you won't! A system that's seriously pressurized can even erupt through the toilet...there are rarely any witnesses, but the person who's pumping the toilet won't enjoy it, plus it makes an awful mess in the head.
If a blocked vent prevents any air from being pulled into the tank by the suction of a pumpout or overboard disharge pump, the pump will pull a vacuum that prevents the pump from pulling out more than a gallon or two at most. A powerful pumpout can even implode a tank.
The two most common locations for a holding tank vent blockage are the vent thru-hull and the other end of the vent line--that end of the hose and the vent fitting on the tank. Start by using a screwdriver blade, ice pick or whatever works to scrape out the vent thru-hull. Then VERY CAREFULLY and with a hose at the ready, open the pumpout fitting cap to relieve any pressure...remove the vent line from the tank and scrape out the end of the hose and the vent fitting on the tank.
If you want to prevent future vent blockages, replace the "vent" thru-hull with an open "bulkhead" thru-hull--the same kind your bilge pump uses. That will allow you to stick a hose nozzle up against it and backflush the vent line every time you wash the boat and/or pump out.
I strongly recommend that both of you get my book (see link in my signature)...it's a comprehensive "marine toilets and holding tanks 101" manual that will not only teach you everything you need to know about how your sanitation system works and how to maintain it, but also how to prevent 99% of problems instead of having to fix 'em. Prevention is not only easier--and often a lot cheaper--than cure, but you get to do preventive maintenance when it's convenient...the need to fix something always occurs at the most INconvenient times!
