Get all posts from db between 2 specified months

Try those args:

'date_query' => array(
    //start date
    array(
        'year' => $startyear,
        'month' => $startmonth,
        'compare' => '>='
    ),
    //end date
    array(
        'year' => $endyear,
        'month' => $endmonth,
        'compare' => '<='
    )
),