It is not possible to capture both image and video using the same intent, Your options are
1) Create your own camera this repo can be a good start But it is going to be a too much effort.
2) Use the Chooser Intent and pass the intent for both image and video, this will give you the option to choose between application which record video and camera separately. In this you cannot do both the things at same time but can choose application according to what you want to do, capture an image or record a video. Below is the code that works for me.
Intent takePictureIntent = new Intent(MediaStore.ACTION_IMAGE_CAPTURE);
Intent takeVideoIntent = new Intent(MediaStore.ACTION_VIDEO_CAPTURE);
Intent chooserIntent = Intent.createChooser(takePictureIntent, "Capture Image or Video");
chooserIntent.putExtra(Intent.EXTRA_INITIAL_INTENTS, new Intent[]{takeVideoIntent});
startActivityForResult(chooserIntent, CAPTURE_MEDIA_RESULT_CODE);