I came to USA with an H1b Visa, my family's H4 visa was also issued with me. After coming to USA I transferred my H1b visa to new company and I got my transfer approved and I got a new H1b with new I-94, my question is whether they can travel with the old H4 or not?
If their visa is still valid, they can travel. Each time an H-1 holder changes jobs, the H-4 holders are NOT required to change their H-4, as long as the H-4 status (I-94) or visa is still valid. An action on H-4 is required only if the status (if within USA) or the visa (if traveling abroad or outside USA) is about to expire. Of course, if H-1 holder has been out of status even for one day, my answer would change.