Follows on from the previous chapter
SHIELD had doctors galore on staff; psychiatrists, physiotherapists, surgeons, even dentists, but they did not have any obstetricians.
When Natasha found out she was pregnant, her and Clint had to visit a local hospital to receive check-ups, scans and treatment. SHIELD set them up with ALIAS' under the names Julie and Michael Williams, complete with a full (slightly fabricated) medical history.
But when they showed up to their 20 week appointment; Natasha's arm in a sling, broken wrist and a black eye (a bad reconnaissance mission had resulted in Natasha being thrown through a second storey window), Michael Williams was reported to the police and social services, he was banned from the hospital until a full investigation was carried out, and several safeguarding measures were put into place for Julie Williams and her baby.
Between them; Hill and Coulson eventually persuaded Fury to hire an OBGYN, and later; a paediatric doctor.
Fury may not exactly be happy about his top two field agents having a baby together, but he had a soft spot for them. He liked to see them happy; and they were happiest when they were together.