usually,they need
all F1 documents,(I-20,I-94card,Trans,Passports etc.)
H1's I797C approval notice with I-94card, marriage certificate.W-2/pay stubs/3 months bankstatements with both of your name to show you have enough money to stay here.
wrote a letter to USCIS stated that you want to change from F1 to H4.
you don't need your LD's company to do it..of course, if they didn't charge on you, it is easier.