Inline Form nested within Horizontal Form in Bootstrap 3

Another option is to put all of the fields that you want on a single line within a single form-group.

See demo here

<form class="form-horizontal">
    <div class="form-group">
        <label for="name" class="col-xs-2 control-label">Name</label>
        <div class="col-xs-10">
            <input type="text" class="form-control col-sm-10" name="name" placeholder="name"/>
        </div>
    </div>

    <div class="form-group">
        <label for="birthday" class="col-xs-3 col-sm-2 control-label">Birthday</label>
        <div class="col-xs-3">
            <input type="text" class="form-control" placeholder="year"/>
        </div>
        <div class="col-xs-3">
            <input type="text" class="form-control" placeholder="month"/>
        </div>
        <div class="col-xs-3">
            <input type="text" class="form-control" placeholder="day"/>
        </div>    
    </div>
</form>

I have created a demo for you.

Here is how your nested structure should be in Bootstrap 3:

<div class="form-group">
    <label for="birthday" class="col-xs-2 control-label">Birthday</label>
    <div class="col-xs-10">
        <div class="form-inline">
            <div class="form-group">
                <input type="text" class="form-control" placeholder="year"/>
            </div>
            <div class="form-group">
                <input type="text" class="form-control" placeholder="month"/>
            </div>
            <div class="form-group">
                <input type="text" class="form-control" placeholder="day"/>
            </div>
        </div>
    </div>
</div>

Notice how the whole form-inline is nested within the col-xs-10 div containing the control of the horizontal form. In other terms, the whole form-inline is the "control" of the birthday label in the main horizontal form.

Note that you will encounter a left and right margin problem by nesting the inline form within the horizontal form. To fix this, add this to your css:

.form-inline .form-group{
    margin-left: 0;
    margin-right: 0;
}

This Bootply example seems like a much better option. Only thing is that the labels are a little too high so I added padding-top:5px to center them with my inputs.

<div class="container">
<h2>Bootstrap Mixed Form <p class="lead">with horizontal and inline fields</p></h2>
<form role="form" class="form-horizontal">
    <div class="form-group">
        <label class="col-sm-1" for="inputEmail1">Email</label>
        <div class="col-sm-5"><input type="email" class="form-control" id="inputEmail1" placeholder="Email"></div>
    </div>
    <div class="form-group">
        <label class="col-sm-1" for="inputPassword1">Password</label>
        <div class="col-sm-5"><input type="password" class="form-control" id="inputPassword1" placeholder="Password"></div>
    </div>
    <div class="form-group">
        <label class="col-sm-12" for="TextArea">Textarea</label>
        <div class="col-sm-6"><textarea class="form-control" id="TextArea"></textarea></div>
    </div>
    <div class="form-group">
        <div class="col-sm-3"><label>First name</label><input type="text" class="form-control" placeholder="First"></div>
        <div class="col-sm-3"><label>Last name</label><input type="text" class="form-control" placeholder="Last"></div>
    </div>
    <div class="form-group">
        <label class="col-sm-12">Phone number</label>
        <div class="col-sm-1"><input type="text" class="form-control" placeholder="000"><div class="help">area</div></div>
        <div class="col-sm-1"><input type="text" class="form-control" placeholder="000"><div class="help">local</div></div>
        <div class="col-sm-2"><input type="text" class="form-control" placeholder="1111"><div class="help">number</div></div>
        <div class="col-sm-2"><input type="text" class="form-control" placeholder="123"><div class="help">ext</div></div>
    </div>
    <div class="form-group">
        <label class="col-sm-1">Options</label>
        <div class="col-sm-2"><input type="text" class="form-control" placeholder="Option 1"></div>
        <div class="col-sm-3"><input type="text" class="form-control" placeholder="Option 2"></div>
    </div>
    <div class="form-group">
        <div class="col-sm-6">
            <button type="submit" class="btn btn-info pull-right">Submit</button>
        </div>
    </div>
</form>
<hr>
</div>