I'm going to echo the advice already given: be available however she needs you when she needs you, but give her the space to come to you. I also agree that it would be good to let the father know you're there for him, too. At a time like this, it's easy for the father to get lost in the shuffle as everyone does their best to comfort the grieving mother.
It's hard, sometimes, to accept that the best thing you can do is wait for them to come to you. If they don't come to you, then reiterate your offer gently in a few days. Don't crowd, but make sure it's very clear you're there whenever they need you in whatever way they need you. It's not an easy balancing act, but it can be done. And whether or not they turn to you, your friends probably appreciate your willingness to help out more than you know.