If I claim 2 dependents on my pay check every 2 weeks can my husband still claim both of our children at the end of the year on his taxes?

[xmasbaby0]

The W-4 you gave your employer does not dictate how you file your tax return.  It just affects how much tax the employer withholds from your paycheck.  

But you asked "can my husband still claim both of our children at the end of the year on his taxes?"  WHY are you filing separate returns?

If you were legally married at the end of 2017 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 each receive the $4050 personal exemption, plus the married filing jointly standard deduction of $12,700 (add $1250 for each spouse over the age of 65).  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.  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.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states