Combining must_not in ElasticSearch Query

If you want simple AND-behavior, then just nest another bool query inside of it:

"query": {
  "bool": {
    "must_not": [
      {
        "bool": {
          "filter": [
            {
              "term": {
                "bool-facet.criteria1": false
              }
            },
            {
              "term": {
                "bool-facet.criteria2": false
              }
            }
          ]
        }
      }
    ]
  }
}

Note that by using the filter (as it's a yes/no question with no scoring needed, but if you wanted scoring, then you would use must instead of filter) you get the desired AND behavior. This changes the question to "not(any document that has criteria1 == false AND criteria2 == false)".

Since updating elasticsearch version was not possible I had to find another solution. This is what worked for me:

"query": {
    "bool": {
        "must_not" : [
            {
                "query": {
                    "bool": {
                        "must": [
                            {
                               "term": {
                                 "bool-facet.criteria1": false
                               }
                            },
                            {
                               "term": {
                                 "bool-facet.criteria2": false
                               }
                            }
                        ]
                    }
                }
            }
        ]
    }
}

The following arrangement worked for me on a similar query in 5.5.1:

"query": {
    "bool": {
        "must": [
            {
                "bool":{
                    "must_not":{
                        "term":{
                            "bool-facet.criteria1": false
                        }
                    }
                }
            },
            {
                "bool":{
                    "must_not":{
                        "term":{
                            "bool-facet.criteria2": true
                        }
                    }
                }
            }
        ]
    }
} 

The other answers may have been correct for other versions, but did not work for me in 5.5.1.