It always the missions to other countries that make Ayame and Teuchi nervous. Missions to other countries means Naruto won't be around for weeks, or possibly months. Missions to other countries means Naruto could die and they wouldn't know until his name appears on the cenotaph. Or until Tsunade's horrified scream rips through the village. But either way, missions to other countries means they might never see Naruto again.
He always stops by on the eve of his mission. He doesn't say much, just announces he has a mission and makes a vague reference to where he's going. He never tells them details, never wanting to compromise their safety. Or maybe he doesn't want them to know what he will be doing in the immediate future. No matter how many times they greet him with delighted voices and fresh, steaming bowls of ramen, Naruto will always think they will think less of him for some of the things he does.
Naruto forgets sometimes, that Teuchi and Ayame both were born and raised in ninja villages. That they have some idea what the village asks of him and they will never condemn him for it.
At the news, both will sober slightly, but do their best to hide it. Teuchi will slide one last bowl across the counter, the 'on the house' going unspoken. The promise hidden in Naruto's, 'I'll pay when I get back', also goes unspoken but everyone hears it anyway. Ayame makes him promise to be careful and to write (messenger birds are a perfectly valid form of communication, Naruto, so use them).
They both know he'll only fulfil one of her promises.
A messenger bird always arrives four days after he leaves.
After the long mission, Naruto always arrives home in the late afternoon, after travelling all day. It would make sense for him to travel during the night, so he can travel discretely and not during the hottest parts of the day. He has his reasons though. Sometimes it's because his team has left a less-than-favourable impression on the village they've aided (although that's rarely a result of the missions Naruto is assigned to). Sometimes it's because Konoha wants them back as soon as possible.
Often, in Naruto's case, he just wants to get home before nightfall.
The day's heat is fading when Naruto steps through Konoha's gates. His first action is to hand in his mission report and visit Tsunade, to reassure her that he is unharmed and his heart is still thumping steadily in his chest. Then he goes home. Showers. Changes. Unpacks. Doesn't eat.
The sun is setting when he walks into the ramen bar. His greeting is tired but heartfelt and it goes ignored by the patrons finishing their meals. This never bothers Naruto because Teuchi and Ayame's faces always light up at the sound of his voice.
He practically collapses onto his favourite stool and moments later a bowl of ramen is pushed across the counter. He thanks Teuchi whole-heartedly and digs in at a pace slower than he does in the day.
By the time his second bowl is finished, he is their only patron. Ayame wipes down the last table, dumps the dishes in the sink and slides onto the stool next to Naruto. Teuchi continues to cook ramen, knowing Naruto is far from finished. He stands over the cooking food, splitting his attention between it and the two teenagers at the counter because Naruto has begun to talk.
It is now that he shares details and even now he keeps some things back. He doesn't tell how he achieved the specifics of the mission; those details are filed away far from the light of day. Instead he talks about the sights he saw, the people he met, the techniques he mastered while away.
Ayame laps it all up. While Naruto talks its easy to ignore the ugly side of his life, easy to put aside her worries of what his job will do to him. He makes it easy for her, describing the mountain range he crossed, the way the land had fallen away from it (I could see everything, even Konoha!). He describes the ramen at the bars he ate at (nowhere near as good as this, and Teuchi preens), the old man who had hired him (pervert), the village's token prodigy (bastard) and the girl who was his guide (nice, but had a really red face. Do you think there was something wrong with her?)
Naruto finishes his last bowl while detailing the technique he mastered while away and the amount of people he proved wrong when it worked (at least seven, but I reckon that bastard counts as two, so eight). Ayame and Teuchi make the suitable impressed noises that are completely sincere and Ayame wrangles a promise out of him to show her his new technique in the near future.
They shake on it, their own, special shake. Slap palms, touch fingertips, link pinkies, point at each other. It looks ridiculous and they also laugh when they do it, while Teuchi looks on with a smile.
Naruto slides his money across the counter, which Teuchi accepts without argument (took Naruto six months to make him do that). Teuchi doesn't bother counting it, trusting Naruto implicitly. And even without counting he knows there will be money for a bowl eaten weeks ago, or even months ago. The fulfilment of Naruto's promise to him.
They watch Naruto walk off until the darkness swallows him up. That night they sleep easier than they've been doing so for weeks or even months.