Mixed insulins do indeed contain a slow and a fast acting insulin - you can get different percentages of each normally they have a numbered incorporated in the name so Nova Mix 30 or something like that, meaning 30% is made up of quick acting insulin (that's from a very hazy memory!). Usually you are told to inject it at breakfast and at tea time and means you have to be very regimented around eating times. MDI gives you the flexibility to eat (or not) when you want and how many carbs you consume.
You don't say what Type of diabetes you have, but NICE guidelines say T1s should be on a MDI regime really - although if it works for you then don't fix it.
T2s can be diet, tablet, long acting only or MDI controlled - or a mixture of those.
It has insulins used for the basal/bolus regime, but if it's a mixed insulin and you're injecting it twice a day (which is normal) then no, it's not basal/bolus.
Basal/bolus refers to a specific injection regime.