If you live with your spouse anytime during the last 6 months of the year then that is NOT a valid method ... you both will either file jointly or separately ... neither can claim HOH.
If you are legally married and living together in the same houshold, NO it is not correct.
You both file as Married Filing Joint on only one tax return. Or you file as Married Filing Separately and he files as Married Filing Separately, two separate tax returns.
That is totally up to you however each child can only be reported on ONE return.
I highly recommend you review the differences between filing jointly and separately BEFORE either of you file a return since separately is rarely the best way to file.
Do you want to lose a bunch of child-related credits? You will if you file MFS.
If you were legally married at the end of 2019 your filing choices are married filing jointly or married filing separately.
Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $24,400 (+$1300 for each spouse 65 or older) You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit.
If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states: AZ, CA, ID, LA, NV, NM, TX, WA, WI)
If you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.