divorce/debt

If the business were a partnership (not an LLC, an actual partnership), then all partners (e.g. both spouses, if the spouses were partners in it) are responsible for the debt.
If the business were an LLC or a corporation, then the owners are NOT responsible for most business's debts (exceptions listed below)--the whole point of an LLC or corporation is to protect the owners from business debts, obligations, and liabilities. So in this case, neither would be affected by the business debt.
Exceptions, where the owners of an LLC or corporation can be responsible for debts:
1) Any debts they personally guaranteed;
2) "Business" credit cards taken out in their own name (if they personally signed the credit card agreement, they are responsible for the charges);
3) Certain "fiduciary" tax debts, such as sales or payroll taxes, where the owner responsible for administrating/overseeing collecting and remitting the taxes is responsible for them;
4) If the owners did not respect the independent existence of the LLC or corporation and instead used it as an extension of their own finances (e.g. no real boundaries between their business and them as persons), in which case creditors may be able to "piece the corporate veil" and bypass the LLC/corporate protection;
5) Amounts owed not soley by the business but also by an owner for his/her own personally wrongful behavior (e.g. if you run someone over while driving a company vehicle for work, the company is liable as your employer--but you would also be liable for being the negligent or careless driver).