In the first 30 days

Employees should add the child to their insurance policy. Most insurance plans give a certain period (often 30 days) to add a baby onto a plan. Be sure to communicate the expectations early so that parents can plan and avoid the hassle of denied claims for new baby's medical expenses.
Set up a plan with employees to revisit their insurance plan. Having a child qualifies for special enrollment, so employees should take advantage of this change. If their current plan does not fit the needs of their growing family, then the policyholder can change plans to one that is better suited to cover their family's needs. Additionally, premiums usually go up with a child, so it would be worth looking into an HSA-qualified plan (or increasing contribution levels to an HSA if you already have one).

In the first year

Encourage employees to use their Health FSA or HSA funds. FSA and HSA dollars can be used for certain baby care supplies such as thermometers, band-aids, pain and gas relief, diaper ointment, breast pumps, sunscreen, first aid kits and more.
Revisit savings goals with the newest addition in mind. A new baby means increased costs, but this shouldn't prevent employees from saving for the future. Share how to utilize their HSA and save what is possible because children often bring the unexpected.

Prepare finances for the entire family. Raising a child for 18 years can cost upwards of $250,000. Share the benefits in planning ahead for the increase in costs to help ease the burden on employees' household budgets.‍
Communicate the benefits of a Dependent Care FSA. DCFSA's are a great way for employees to receive childcare and save money once they go back to work. These accounts allow employees to set aside pre-tax funds for eligible dependent services, such as preschool, summer day camp, and before or after school programs in addition to child/adult daycare.
Employees need to invest in the future. If an employee doesn't have an HSA, it's worth the time to look into one. Not only does it save employees money each month, but the pre-tax money saved can be invested and grow so that there's even more for the future. While an HSA should not replace a 401(k) plan, it can be used to augment retirement funds when the time comes.

In the end, to best support employees growing families, it can help keep some simple concepts in mind:

With discipline and planning, employees will have more money to support a growing family.