You are equally responsible for all debts acquired during the marriage, including tax debt.
Note that the government (or other creditor) will come after who's ever name is on the debt BUT according to family law all debt has to be split equally, as with all assets acquired during the marriage regardless of whose name is on what.
As for his company tax debt, the same is true, it is an asset or liability of the marriage, that he happens to own, but it is equally yours.
If his company was worth a lot of money I am sure you would want half of that. In the same manner the tax debt should be shared too.
Even though you are not a shareholder or director, you are entitled to half of the company value (positive or negative).
All assets and debts acquired during the marriage are split equally. Simple.
Lots of (unscrupulous or stupid) people try to assign debt to the other, but want half the assets. Simply unfair and against family law.