Return an array of array of arrays of objects

Here is some code that retrieves the data from each table in separate arrays, and then builds the final data structure from it.

It is quite generic, as you only have to specify which fields are the common keys (primary and foreign keys, which are assumed to have the same name) for each pair of tables:

function loadTable($dbh, $table) {
    // Perform simple table select, and return result set
    $sth = $dbh->prepare("SELECT * FROM $table");
    $sth->execute();
    $rows = $sth->fetchAll(PDO::FETCH_ASSOC);
    return $rows;
}

function connectChildren($parents, $children, $name, $common_keys) {
    /* Returns $parents array, but with each element extended with
     * a $name key, which is an array of matching $children elements.
     * The match is made by comparing the values for each of the $common_keys 
     * in both arrays.
     * When a $children element is added to the $name array, its $common_keys
     * are removed from it as they are already known in the $parents element.
     * (this removal behaviour is optional and could be left out)
     */ 
    $index = [];
    // Build a temporary index to associate $parents elements by their 
    // primary key value (can be composite) 
    foreach ($parents as $i => $parent) {
        $primary_key = [];
        foreach ($common_keys as $common_key) {
            $primary_key[] = $parent[$common_key];
        }
        $index[implode("|", $primary_key)] = $i;
        $parents[$i][$name] = [];
    }
    // Main algorithm: inject $children into $parents
    foreach($children as $child) {
        $foreign_key = [];
        // Collect foreign key value
        foreach ($common_keys as $common_key) {
            $foreign_key[] = $child[$common_key];
            // Remove foreign key from child
            unset($child[$common_key]);
        }
        // Find the corresponding $parents element via the index
        $i = $index[implode("|", $foreign_key)];
        $parents[$i][$name][] = $child;
    }
    return $parents;
}

// Step 1: load all the table data    
$rows_dep = loadTable($dbh, "departments");
$rows_job = loadTable($dbh, "jobs");
$rows_peep = loadTable($dbh, "peeps");


// Step 2: connect the data, layer by layer, in bottom-up order:    
$rows_job = connectChildren($rows_job, $rows_peep,
                            "peeps", ["deperatment_id", "job_id"]);
$rows_dep = connectChildren($rows_dep, $rows_job,
                            "jobs", ["deperatment_id"]);

print_r ($rows_dep);

Output on the test data:

Array
(
  [0] => Array
    (
      [deperatment_id] => 1
      [department_name] => HR
      [jobs] => Array
        (
          [0] => Array
            (
              [job_id] => 1
              [job_name] => Idiot
              [peeps] => Array
                (
                  [0] => Array
                    (
                      [peep_name] => Smith
                    )
                )
            )
          [1] => Array
            (
              [job_id] => 2
              [job_name] => Fool
              [peeps] => Array
                (
                  [0] => Array
                    (
                      [peep_name] => Jones Major
                    )

                  [1] => Array
                    (
                      [peep_name] => Jones Minor
                    )

                )
            )
        )
    )
  [1] => Array
    (
      [deperatment_id] => 2
      [department_name] => Software
      [jobs] => Array
        (
          [0] => Array
            (
              [job_id] => 4
              [job_name] => Software guru
              [peeps] => Array
                (
                  [0] => Array
                    (
                      [peep_name] => Mr. In-the-wrong-department
                    )

                  [1] => Array
                    (
                      [peep_name] => Mawg
                    )
                )
            )
          [1] => Array
            (
              [job_id] => 5
              [job_name] => PFY
              [peeps] => Array
                (
                  [0] => Array
                    (
                      [peep_name] => William Topaz McGonagall
                    )
                )
            )
        )
    )
  [2] => Array
    (
      [deperatment_id] => 3
      [department_name] => Accounts
      [jobs] => Array
        (
          [0] => Array
            (
              [job_id] => 6
              [job_name] => Number cruncher
              [peeps] => Array
                (
                  [0] => Array
                    (
                      [peep_name] => Blaise Pascal
                    )
                  [1] => Array
                    (
                      [peep_name] => Isaac Newton
                    )
                )
            )
        )
    )
)

You could then proceed with json_encode($departments), etc.