I want to invest in a bank's share, but I know the bank earns interest as a source of income. But it does have other sources of income too. Will it be haram for me to invest in it knowing that it earns interest?
It is haram to invest when there is interest involved. Interest is called riba in arabic and interest on investment or loan is called riba an-nasiya which means an excess charged for a loan in cash or kind which is haram. As for your condition, if you do not make interest on your investments, you can do business with them as long as you follow shria.
Every transaction or investment that contains interest/riba is not allowed in Islam. Maybe you interesting to do sharia investment called Mudharabah and Musyarakah