I successfully solved my problem. Here is my code:

The complex JSON object:

   {
    "medications":[{
            "aceInhibitors":[{
                "name":"lisinopril",
                "strength":"10 mg Tab",
                "dose":"1 tab",
                "route":"PO",
                "sig":"daily",
                "pillCount":"#90",
                "refills":"Refill 3"
            }],
            "antianginal":[{
                "name":"nitroglycerin",
                "strength":"0.4 mg Sublingual Tab",
                "dose":"1 tab",
                "route":"SL",
                "sig":"q15min PRN",
                "pillCount":"#30",
                "refills":"Refill 1"
            }],
            "anticoagulants":[{
                "name":"warfarin sodium",
                "strength":"3 mg Tab",
                "dose":"1 tab",
                "route":"PO",
                "sig":"daily",
                "pillCount":"#90",
                "refills":"Refill 3"
            }],
            "betaBlocker":[{
                "name":"metoprolol tartrate",
                "strength":"25 mg Tab",
                "dose":"1 tab",
                "route":"PO",
                "sig":"daily",
                "pillCount":"#90",
                "refills":"Refill 3"
            }],
            "diuretic":[{
                "name":"furosemide",
                "strength":"40 mg Tab",
                "dose":"1 tab",
                "route":"PO",
                "sig":"daily",
                "pillCount":"#90",
                "refills":"Refill 3"
            }],
            "mineral":[{
                "name":"potassium chloride ER",
                "strength":"10 mEq Tab",
                "dose":"1 tab",
                "route":"PO",
                "sig":"daily",
                "pillCount":"#90",
                "refills":"Refill 3"
            }]
        }
    ],
    "labs":[{
        "name":"Arterial Blood Gas",
        "time":"Today",
        "location":"Main Hospital Lab"      
        },
        {
        "name":"BMP",
        "time":"Today",
        "location":"Primary Care Clinic"    
        },
        {
        "name":"BNP",
        "time":"3 Weeks",
        "location":"Primary Care Clinic"    
        },
        {
        "name":"BUN",
        "time":"1 Year",
        "location":"Primary Care Clinic"    
        },
        {
        "name":"Cardiac Enzymes",
        "time":"Today",
        "location":"Primary Care Clinic"    
        },
        {
        "name":"CBC",
        "time":"1 Year",
        "location":"Primary Care Clinic"    
        },
        {
        "name":"Creatinine",
        "time":"1 Year",
        "location":"Main Hospital Lab"  
        },
        {
        "name":"Electrolyte Panel",
        "time":"1 Year",
        "location":"Primary Care Clinic"    
        },
        {
        "name":"Glucose",
        "time":"1 Year",
        "location":"Main Hospital Lab"  
        },
        {
        "name":"PT/INR",
        "time":"3 Weeks",
        "location":"Primary Care Clinic"    
        },
        {
        "name":"PTT",
        "time":"3 Weeks",
        "location":"Coumadin Clinic"    
        },
        {
        "name":"TSH",
        "time":"1 Year",
        "location":"Primary Care Clinic"    
        }
    ],
    "imaging":[{
        "name":"Chest X-Ray",
        "time":"Today",
        "location":"Main Hospital Radiology"    
        },
        {
        "name":"Chest X-Ray",
        "time":"Today",
        "location":"Main Hospital Radiology"    
        },
        {
        "name":"Chest X-Ray",
        "time":"Today",
        "location":"Main Hospital Radiology"    
        }
    ]
}

The jQuery code to grab the data and display it on my webpage:

$(document).ready(function() {
var items = [];

$.getJSON('labOrders.json', function(json) {
  $.each(json.medications, function(index, orders) {
    $.each(this, function() {
        $.each(this, function() {
            items.push('<div class="row">'+this.name+"\t"+this.strength+"\t"+this.dose+"\t"+this.route+"\t"+this.sig+"\t"+this.pillCount+"\t"+this.refills+'</div>'+"\n");
        });
    });
  });

  $('<div>', {
    "class":'loaded',
    html:items.join('')
  }).appendTo("body");

});

});

Every object has to be named inside the parent object:

{ "data": {
    "stuff": {
        "onetype": [
            { "id": 1, "name": "" },
            { "id": 2, "name": "" }
        ],
        "othertype": [
            { "id": 2, "xyz": [-2, 0, 2], "n": "Crab Nebula", "t": 0, "c": 0, "d": 5 }
        ]
    },
    "otherstuff": {
        "thing":
            [[1, 42], [2, 2]]
    }
  }
}

So you cant declare an object like this:

var obj = {property1, property2};

It has to be

var obj = {property1: 'value', property2: 'value'};