Thumi=Tumi (Bengali)=you
wholo= holo (Bengali)=are
Mere Jaan= Meri Jaan (Urdu)= darling

I do not know the source of this sentence. But definitely it is a dialog of a Britisher of East India Company or imperial Britain who came India to perform his duty that is why his sentence becomes cocktail of Bengali and Urdu languages. Generally these British servants reported at their head quarters where they had to learn one major Indian language. Generally it was Hindusthani (a language mixed with Hindi and Urdu), the language which was spoken by Indian soldiers of British army. Afterwards the person came in Bengal and learned local Bengali language. In Urdu and Hindi this sentence is - Tum ho meri jaan. As he learned Urdu at first, he used auxiliary verb are (ho in Hindi and Urdu; holo in Bengali) which is not used in Bengali. Another point is they used th in place of t. So Bengali tumi became thumi.