In my mortgage redraw account. So it saves me on interest, access to cash within 2 business days (no upper or lower limits on amount, no restrictions on number of deposits or withdrawals) and I don't pay tax, which I would if I had my savings in an online savings account.
When we pay the mortgage off, we will have a hefty cash emergency fund in 1 or 2 online savings accounts or rolling term deposits, depending on interest rates and annoyance level. Not sure whether it will make any difference tax-wise splitting the emergency fund between me and DH or whether it doesn't matter if it's all in one name. However, my risk of death in the next 10 years is higher than average so maybe it will make sense to split emergency funds half in my name, half in his name so that whatever happens, one of us has insta-access to $$$.