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.  

Hi @Muk6202! Congratulations on your new business! If you do plan to file jointly and your spouse has regular income tax withholding, you may not need to make separate quarterly tax payments, if his withholding is enough to cover your joint liability for the year, including your self-employment income. Keep in mind, though, that the income you earn from independent contracting work is subject to self-employment tax in addition to regular income tax. This means your tax liability may increase more than you expect based on your net self-employment earnings. Also, be sure to keep good records of your expenses, as these can be used to lower your business income and therefore your income tax and self-employment tax liability. If you'd like to check to see if his withholding is on track to cover you or if you should consider boosting it or making quarterly payments, the IRS withholding estimator is an awesome tool to use!