First try to understand the jurisdiction of High Court in respect of Transfer Petitions. A District Court has got the power to transfer a case from one coourt to another court within its District. Similarly, a High court has got power to transfer petition from one court falling in one district to another court falling in another district within the State. If case has to be transferred from one state to another state only Supreme Court has got the power.
Now you filed a case in Metropolitan Court. Your husband filed a transfer petition in Bombay High Court seeking transfer from the metropolitan court, where you filed to some other court (where he might be residing or living for gain). I presume that your court as well as his court fall within the state of Maharashtra but in different districts.
Go to Bombay High Court web site. There you can trace the next date of hearing by properly typing the number of the case he filed, or by typing petitioner's (his) name or by typing respondent's name. You may get the information you require. There is another method. If he really filed the transfer petition, you check your address on that petition. If it is correct you will get a court notice for transfer petition intimating the next date of hearing.
Now, how to tackle this transfer petition. Generally, husband's transfer petitions will not get favourable orders. But you should not leave it to chance. By just sending your reply rejecting the transfer petition in the post will not be entertained by the court. Proper reply with solid grounds that why his petition should not be allowed has to be prepared as per the procedure laid down by Bombay High Court and in advance has to be filed in the court's registry (in general terms court office) and on the date of hearing put oral submissions on the basis of the reply already filed by you. You can do it yourself or you can engage an advocate for preparation of reply and also to put oral arguments in favour of you and also appraise you of the condition of the case from time to time.
As you are senior engineer, I suggest you to engage a good sincere and honest advocate to defend your position.
Warm regards