See the Catechism of the Catholic Church, paragraph 2180-2181 (emphasis added):
The precept of the Church specifies the law of the Lord more precisely: “On Sundays and other holy days of obligation the faithful are bound to participate in the Mass.” “The precept of participating in the Mass is satisfied by assistance at a Mass which is celebrated anywhere in a Catholic rite either on the holy day or on the evening of the preceding day.”
The Sunday Eucharist is the foundation and confirmation of all Christian practice. For this reason the faithful are obliged to participate in the Eucharist on days of obligation, unless excused for a serious reason (for example, illness, the care of infants) or dispensed by their own pastor. Those who deliberately fail in this obligation commit a grave sin.
As baltobetsy stated, caring for the sick is a valid ‘serious reason’ to miss Mass, and thus no dispensation is needed and he has committed no sin. If he has any doubt of this, he can of course always speak to his Priest to confirm it.
Now hypothetically, if my wife had a bad cold and I decided to skip Mass to ‘take care of her’…then sat at home watching TV…well, that’s another matter. But from your description it doesn’t sound anything like that ;).
God bless you, and congratulations to your friend and his wife on the birth of their child!