You can use wildcards to query multiple child fields, like this: party.contacts.*.
The full query would look like this:
{
"query": {
"multi_match": {
"query": "ram",
"fields": [
"invoice_number",
"status",
"party.display_name",
"party.contacts.*"
]
}
},
"sort": {
"created_at": "desc"
}
}