If you have rented out your own house and live in a rented place yourself, you are eligible for both income tax benefits and HRA benefits but the rent that you receive is added to your taxable income. Also in case of rented property, you claim a deduction on account of repairs and maintenance.
If you take a joint home loan with your child or spouse, you all can avail these benefits of tax rebates. The tax benefits are applicable in accordance with the proportion of loan taken by everyone in a joint loan. For instance, if the ownership is in the ratio 70%:30 % and you have borrowed an amount of 50 lakh, it would be split into 35 lakh and 15 lakh respectively and the interest would be calculated accordingly.
Obtaining a home loan certainly manages your taxes but you should not go for a home loan only to avail tax benefits. It is always recommended to use your own funds to buy a fixed asset and save the money that you would have paid as equated monthly instalments. Instead you can invest this money in a financial instrument that earns you a good rate of interest.