In dictionary,

with /wɪð, wɪθ/ ●●● S1 W1 preposition

2 having, possessing, or carrying something

a tall gentleman with a beard

a book with a green cover

a man with a gun

We need someone with new ideas.

Only people with plenty of money can afford to shop here.

She came back with a letter in her hand.

So, if I say "I am having rice with chicken and broccoli", does it mean that "They are all in a plate" as in this picture:

But Asian people often have dishes separately.

Let say a man have this meal (3 separated dishes) as showed in the following picture:

SO, would the man be wrong if he said: "I am having rice with chicken and broccoli"?