Python logging into file as a dictionary or JSON

I am trying to set up logging where I can log in both stdout and on to a file. This i have accomplished using the following code:

logging.basicConfig(
        level=logging.DEBUG, format='%(asctime)-15s %(levelname)-8s %(message)s',
        datefmt='%a, %d %b %Y %H:%M:%S', handlers=[logging.FileHandler(path), logging.StreamHandler()])

The output of this something like this:

2018-05-02 18:43:33,295 DEBUG    Starting new HTTPS connection (1): google.com
2018-05-02 18:43:33,385 DEBUG    https://google.com:443 "GET / HTTP/1.1" 301 220
2018-05-02 18:43:33,389 DEBUG    Starting new HTTPS connection (1): www.google.com
2018-05-02 18:43:33,490 DEBUG    https://www.google.com:443 "GET / HTTP/1.1" 200 None

What I am trying to accomplish is logging this output to a file not as it is printing to stdout, but as a dictionary or JSON object similar to something like this (while keeping the stdout as it is at the moment):

[{'time': '2018-05-02 18:43:33,295', 'level': 'DEBUG', 'message': 'Starting new HTTPS connection (1): google.com'}, {...}, {...}]

Is this doable? I understand that I can post process this log file after my process is finished, but I am looking for a more elegant solution because certain things i am logging are quite big objects themselves.

Answer

So based on @abarnert, i found this Link which provided a good path to making this concept work for the most part. The code as it stands is:

logger=logging.getLogger()
logger.setLevel(logging.DEBUG)

file_handler=logging.FileHandler('foo.log')
stream_handler=logging.StreamHandler()

stream_formatter=logging.Formatter(
    '%(asctime)-15s %(levelname)-8s %(message)s')
file_formatter=logging.Formatter(
    "{'time':'%(asctime)s', 'name': '%(name)s', 
    'level': '%(levelname)s', 'message': '%(message)s'}"
)

file_handler.setFormatter(file_formatter)
stream_handler.setFormatter(stream_formatter)

logger.addHandler(file_handler)
logger.addHandler(stream_handler)

Although it does not fully meet the requirement, it doesnt require any pre processing, and allows me to create two log handlers.

Afterwards, i can use something like:

with open('foo.log') as f:
    logs = f.read().splitlines()
for l in logs:
    for key, value in eval(l):
        do something ...

to pull dict objects instead of fighting with improperly formatted JSON to accomplish what i had set out to accomplish.

Still am hoping for a more elegant solution.