1. Sir, there are not much lengthy procedure to get medical benefit in case of maternity of wife. However, you must possess ESIC Pehchan Card on which name of your wife must be there. I think, you will make efforts to get the same through your employer/HR.
2. Maternity Benefit is payable only to the covered women ( i.e. to covered woman employee only) and in case of family member i.e. wife only medical facilities are available provided the employee (her husband) is covered under above Act. You are also required to get your wife periodically medically check up from authorised ESI Dispensary Doctor or ESI Hospital to which you are attached and get necessary guidance/medicines etc.
3. In view of above, I hope, you will contact ESIC Branch Office Manager immediately to get the Pehchan Card and please make sure that on said Card, the name of your wife and other family members are correctly entered by the said office. Thereafter, you can also contact ESIS dispensary or hospital as per your requirement. With best wishes.