Why use "is" in this sentence "Here is your umbrella and your coat“

The sentence

Here is your umbrella and your coat.

is from New Concept English. So I presume it is grammatically correct.

I also saw sentences like

There is an apple and two oranges.

So why is is used instead of are?

The rule I learnt is that the verb / auxiliary agrees with the first member of the list. E.g.:

There is a black cat, a white cat, and two ginger cats.

There are four cats. One is black, one is white, and two are ginger.

There is is coming to be used as an invariable term to introduce items whether they are singular or plural. The same may also be happening with here is, but in your example 'your umbrella and your coat' can be regarded as a single item, in so far as the two are being offered together.