You say husband as opposed to ex husband or separated husband. If you live together or did live together any part of the last half of 2019, only one of you can claim the child for any tax benefit. So, the answer to your question is no.
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner. You cannot use the special rule if you are filing as Married Filing Separately (MFS). You cannot claim the Earned Income Credit, at all, if you are filing MFS
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.
So, it's good idea to let the other parent know that you will be claiming those items, as many first time divorced parents are not aware of this rule and may try to claim those items, which will cause the IRS to send out letters.
Ref: https://www.irs.gov/publications/p17#en_US_2017_publink1000170897
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You can if you are the custodial parent. The custodial parent is (the parent the child lived with for more than 183 days in 2016.
