I just wanted to day that I think that it's great that you are enabling your child access to both speech (speech-reading, listening skills etc) as well as ASL.
I know in my case, that if I had access to ASL growing up (in addition to speech-reading and listening) it would have been a tremendous advantage personally. My parents did not let me learn ASL because some very well meaning but totally mis0guided "professionals" told them that ASL (or any signing at all) would make me stop speaking, would negatively effect my English and a number of other completely untrue so called "facts" they had been "taught".
Of course we now conclusively know that ASL does not have any negative impact at all... rather it can have a positive impact (it is true that some children may focus on one language more than another temporarily, however this is completely normal, so don't worry. It is the exact same language acquisition process that happens with bilingual/multi-lingual hearing children!).
I am a huge advocate for giving Hoh/d/Deaf children and adults access to as many "communication tools" as is realistically possible. This includes developing speech-reading skills, listening skills (if their is usable hearing), reading & writing skills, Sign Language (&/or visual language aka SEE I/II etc), as well as less common "tools" such as Cuing (a "tool" I've yet to learn).
Just as bilingualism/multilingualism has been proven to be a positive asset for hearing people ... bilingualism/multilingualism & "mode-ism" (ie SEEI,SEEII, Cuing etc) is of benefit to Hoh & d/Deaf children and adults ... the journey can be challenging, however the end result is an individual who is able to clearly communicate, express ideas, are able to learn in the environment of their choice (ie gain a good quality university education if they choose, and have a career of their choosing effectively unlimited by anything other than their hearts desire.
For what it's worth ... I also express a gentle and well-intended word of caution regarding VOICE (and other organizations who subscribe to an "oral only approach"). Hoh/Deaf organizations should support Hoh/d/Deaf by offering assistance in learning a various skill/communication strategy they specialize in without attacking explicitly or otherwise, other communication methods, or stating that their way is the only "right way" or only "responsible choice". While some Hoh/deaf are able to do well with a purely oral approach, many do not.
Multiple communication strategies for Hoh/Deaf should be viewed in the same positive light as multi-lingual (hearing) individuals are. Hearing people fluent in, or at least knowledgeable in two or more languages often have better linguistic skills (including grammar, sentence structure etc), are able to access better & higher paying jobs, and are more freely able to enjoy travel and socialization. In all cases being knowledgeable in more than one language is seen as an asset in the hearing world ... why should it be different just because someone is Hoh/d/Deaf?. It shouldn't.