Even though my parents have been out of Pakistan for 20 odd years they have still retained the desi accent, which will obviously never go away. Over the years there have been such funny situations, where my dad is flirting with a waitress and she doesnt understand a thing hes saying but smiles politely anyway, similarly with my mother.
The worst thing though is when my parents pick up slang words. At home my sisters and I only used to speak in English to each other, and we’d use a lot of slang and often when I got into arguments with my mother Id tell her to ‘chill’ or tell her that my dad is so ‘chilled out’. So my mother starts using the word ‘chill’, but with a desi accent. Its really funny I must say.
My mother understands English well, but can't speak it fluently...Never had a need to, but she knows some phrases and stuff...
So she goes for her passport interview with my sister and the interviewer asks, "Who is the vice president of the United States?" I have no idea what my mother was thinking but she says, "I am...":D...The interviewer started laughing...
Then he asks, "How many stars are in the United States flag, and my mother says, "You tell me..." By this time, my sister tells me that the face of the interviewer had gone red from suppressing his laughter...And the funny thing was, my mother was dead serious and confident when she was answering him...
Then he asks, who was the first president of the United States? My mother says, "Bill Clinton..." This answer was too much and the guy started guffawing...
He asked my mother, "Did you actually prepare for this interview?" To which my mother replies, "Yes, I am educated"...
Needless to say, she got the passport anyways...:D
My Nani came to the states about 10 years ago. My brothers and I all speak with her in punjabi but my mamoo's little girls (4,5 and 8) will only speak in english, so nani ami's picking up english!! it's so cute when she pops out in the middle of punjabi, bacation (vacation), milk, yuse (juice), Thnksgibin, shopping bag, etc...with her accent.
My parents have been in the US for over 30 years and like your parents, Catty, they also speak very good English but with a desi accent. My dad, more so than my mom, uses some slang but it sounds cute. My mom sticks to the more basic English. Of course when they speak to each other, the language is always Punjabi but with us kids, they fluctuate between speaking English some times and Urdu at other times.
my mum is the comedian in my house... and boy she is funny :)
she speaks a lot of english, but at times u just go.. 'huh?'
my bro and sis mix english and urdu together.. and mums picked up on that.. two days ago she was showing me this technique to get imli ka paani... and she goes... 'u see how im malaying this..?' it was sooo funny.. another one shes picked up on is 'garaming' (to heat something up)
My parents have been in Canada for over 30 years. Can you imagine a Paki accent mixed with a Canadian accent? My dad actually says, "Eh" after everything. Even I don't do that. My dad, compared to my mom, is the more colorful in his expressions. He often refers to my brothers as, 'dude'. But the funniest is when my dad sings songs in the shower or car. He doesn't sing the old Bollywood classics. My dad prefers the Golden Oldies that he's been listening to on the radio. It's really cute. Then he asks me questions about these obscure celebrities from his day, like "Lolla Falana and Tony Orlando" and I'm like Who are they?
My mum and dad mix their urdu with dutch. Not just with us but also when they r in Pakistan.
We were in Murrey and dad got us all a softdrink so he asks the guy for ‘rietjes’. And the guy is like errrr? SO my dad repeats himself and all of us start laughing He didn’t even know he was using the dutch word for straws
Yaar…this is kinda sweet and funny too! 
He didn’t even know he was using the dutch word for straws 