If I have a set of MongoDB documents like the following, what can I do to get a find() result that only returns the families who have 2 pets who all like liver?

Here is what I expected to work:

db.delegation.find({pets:2, $and: [{'foods.liver': true}, {'foods.allLike': true}] })

Here is the document collection:

{
    "_id" : ObjectId("5384888e380efca06276cf5e"),
    "family": "smiths",
    "pets": 2,
    "foods" : [ 
        {
            "name" : "chicken",
            "allLike" : true,
        }, 
        {
            "name" : "liver",
            "allLike" : false,
        }
    ]
},
{
    "_id" : ObjectId("4384888e380efca06276cf50"),
    "family": "jones",
    "pets": 2,
    "foods" : [ 
        {
            "name" : "chicken",
            "allLike" : true,
        }, 
        {
            "name" : "liver",
            "allLike" : true,
        }
    ]
}

What I end up getting is both families because they both have at least one food marked as true for allLike. It seems that the two conditions in the $and are true if any foods sub-document matches, but what I want is the two conditions to match for the conditions as a pair.

As is, I get the Jones family back (as I want) but also Smith (which I don't). Smith gets returned because the chicken sub-doc has allLike set to true and the liver sub-doc has a name of 'liver'. The conditions are matching across separate foods sub-docs. I want them to match as a pair on a foods document.

This code is not the real use case, obviously. I have one, but I've simplified it to protect the innocent...