Thank you, Ferghis - too kind!
Now to confuse things.
Personally, as a DM, I get just a little more complicated than that

, but again, the design isn't precisely specified for these cases.
The example I like to use is, a two-man party is exploring along a North-South hallway, while two wandering monsters are wandering along the East-West hallway that intersects a bit up the way.
Able has a Stealth of +5 and a Passive Perception of 15.
Bob has a Stealth of +0 and a Passive Perception of 10.
The orc has a Stealth of +2 and a Passive Perception of 10.
His pet wolf has a Stealth of +4 and a Passive Perception of 17.
As they draw close to the corner, each makes a Stealth roll as follows:
Able 10, +5 = 15
Bob 12, +0 = 12
Orc 9, +2 = 11
Wolf 15, +4 = 19
The orc's 10 Perception does not hear either Bob or Able. The orc is Surprised, and does not participate in the surprise round.
The wolf's keen ears and 17 Perception hear both Bob and Able. The wolf is not surprised, and participates in the surprise round.
Able's 15 Perception hears the orc's boots on the stone floor, but not the wolf's quiet paw pads. Able is not surprised, and participates in the surprise round.
Bob's 10 Perception does not hear either the orc or the wolf. Bob is Surprised, and does not participate in the surprise round.
So, we have Able and the wolf both taking part in a Surprise round while their partners do not.