Yes his withholding counts towards your joint total tax. Yes he can increase his withholding to cover any of your self employment tax.
You pay Self Employment tax (Scheduled SE) on a Net Profit of $400 or more on Schedule C. You pay 15.3% SE tax on 92.35% of your Net Profit (If it is greater than $400). The 15.3% self employed SE Tax is to pay both the employer part and employee part of Social Security and Medicare. So you get social security credit for it when you retire.
