Number of times I have answered such questions regarding inter-religion marriage apart from getting them solemnized before the marriage officer. You both belonging to different religion can marry in the court without changing your individual religion. Court marriage as you call it is solemnized under the Special Marriage Act, 1954 all such marriages can take place between any two Indian citizens as well one Indian citizen with a foreigner irrespective of their religion, caste or creed, and you can say this is the secular form of marriage available in our country. Such a marriage is solemnized before the marriage officer/registrar usually D.C. deputy commissioner of the area /SDM where both or any of the parties to such a marriage reside permanently or for at least one month. Cost of such a marriage as the rate prevalent in your area.
Now how you proceed? Both the parties to the marriage file a joint application before the marriage officer along with individual affidavit attested by notary public specifying the age(boy 21yrs &girl 18yrs), place of residence, marital status(unmarried or divorcee as the case maybe), mental status(not idiot or not with unfit mind), not related to each other. Along with this you have to give proof of age (School certificate, Passport, Pan card), proof of residence (Passport, ration card, voters ID card, rent agreement), & the application of such a marriage should be witnessed by 3 independent adult persons, affix one photograph of each of the parties & all the 3 witnesses.
You have made such an application/notice to the marriage officer in person along with all the 3 witnesses. On receiving such an application the marriage officer issues a month notice regarding the intended marriage & get such a notice affixed on the notice board out side his office, a copy of such notice is sent to the marriage officer under whose jurisdiction the other party lives, also a copy is to the individual parties address. After expiry of the period of notice a date is fixed on which all the persons parties to the marriage & 3 witnesses appear again before the marriage officer who declare them married & issue a certificate to this regard.
Incase of any objections raised the marriage officer will settle these objections. Now what can be objections that can be raised? These can ONLY BE REGARDING THE CONDITIONS NECESSARY FOR SUCH MARIAGE & NOTHING ELSE. What are the conditions? As I stated above i.e. Age, martial status, mental status, prohibited relationship (related to each other by blood). This is the brief & general procedures I have told you here, incase you want any clarification you can ask. It’s always better to engage a lawyer to get such marriage solemnized to avoid any legal impediments which he will be able to handle.