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Yes, you can make the election to file jointly. You can claim your elder child and your newborn child if they meet the requirements to be a dependent. 

• You can claim a non-citizen child as a dependent on your tax return, which would likely entitle you to a dependent credit, if the child meets the IRS definition of a "qualifying child." This is the same standard that applies to children who are citizens.
• Who can I claim as my dependent? (May be qualifying relatives)
• Do you financially support your family living abroad?

To make the Election to File a Joint Return:

• You and your spouse are treated, for federal income tax purposes, as residents for all tax years that the choice is in effect. However, for Social Security and Medicare tax withholding purposes, the nonresident alien may still be treated as a nonresident alien. 
• You must file a joint income tax return for the year you make the choice (but you and your spouse can file joint or separate returns in later years).
• Each spouse must report his or her entire worldwide income for the year you make the choice and for all later years unless the choice is ended or suspended.
• Generally, neither you nor your spouse can claim tax treaty benefits as a resident of a foreign country for a tax year for which the choice is in effect. 
  • Nonresident Spouse - Review this link for additional details
  • Claiming a Noncitizen Spouse and Children on your Taxes

You will need to obtain an ITIN for your newborn.  Your tax return must contain a Form W-7 and it must be mailed. 

• Individual Taxpayer Identification Number (ITIN)