The Quaids' newborn twins Zoe Grace and Thomas Boone were erroneously given a massive overdose of the drug last month while hospitalized at Cedars-Sinai Medical Center in Los Angeles.
The lawsuit claims Baxter is liable and negligent because the packaging of its 10-unit-per-milliliter vial of Heparin closely resembles the 10,000-unit-per-milliliter container of the drug, TMZ.com said.
The couple's attorney, Susan E. Loggans, confirmed the Quaids' babies "were very critical for a while," but are doing well now and "everything looks good."
The infants reportedly went home from the hospital Tuesday.
The Quaids said in their lawsuit that the vials should have been recalled after three children died in Indiana from a similar incident involving an overdose of Heparin, E! Online said.
Filed in Chicago, the Quaids' lawsuit seeks more than $100,000 in damages, but Loggans insisted the case "isn't about money," but more the fact the Quaids don't want other families to suffer the same ordeal they did.