Changing W4 withholding for both parents w/ newborn

Personally I would not change anything on the current old  W-4 forms you have if you get the desired refund now ... adding a dependent will only make it sweeter.  You are not required to change anything on the W-4 at all.   If you are going to change then you both need to change with the new W-4 system  so use this tool to figure it out ... 

Use the Tax Withholding Estimator on the IRS web site to figure out what you and your spouse  should each put on the W-4 forms that you give to your employers. It's much easier than using the worksheets on the form. It will let you adjust your withholding to get the approximate refund amount that you want.

You should consider submitting a new W-4 form so that your tax withholding can be adjusted.

Only one parent can claim the child. And this should be the parent with the higher income.

You can read this TurboTax article for more information.

You can also this TurboTax W-4 calculator to simulate your tax withholding.

Congratulations for your newborn child!

The new W-4 form doesn't use allowances anymore, so you no longer "claim 1" or "claim 0" or any other number of allowances. The new form works differently. Use the Tax Withholding Estimator that Critter-3 recommended to figure out what you should each put on your W-4 forms.

The fact that you both work for the same company doesn't make any difference.

To better understand refund vs liability, see another of my answers here.

@rjs is correct, allowance aren't used anymore. I suggest you go through Tax Withholding Estimator.