edit.html.slim

= simple_form_for @profile, url: my_membership_path, html: { class: "form-horizontal" } do |form|
  = form.simple_fields_for @profile.customer do |fields|
    = fields.input :first_name
    = fields.input :last_name, label: false
  = form.simple_fields_for @profile.user do |fields|
    = fields.input :email
    = fields.input :password
  = form.simple_fields_for @profile.customer do |fields|
    = fields.input :zip_code
  .form-actions
    = form.button :submit, class: "btn btn-primary"

my_memberships_controller.rb

class MyMembershipsController < ApplicationController
  respond_to :html

  def edit
    @profile = Profile.find(current_customer)
  end

  def update
    @profile = Profile.find(current_customer)

    if @profile.update_attributes(profile_params)
      flash[:notice] = t("flash.my_membership.update.notice")
      respond_with current_customer, location: my_subscriptions_path
    else
      flash[:alert] = t("flash.my_membership.update.alert")
      render "edit"
    end
  end

private

  def profile_params
    params.require(:profile).permit(
      customer: [
        :first_name,
        :last_name,
        :zip_code ],
      user: [
        :email,
        :password ] )
  end

end

profile.rb

class Profile
  include ActiveModel::Model

  attr_reader :customer
  attr_reader :user

  def self.find(customer)
    new(customer, customer.user)
  end

  def initialize(customer, user)
    @customer = customer
    @user = user
  end

  def persisted?
    true
  end

  def update_attributes(params)
    customer.with_transaction_returning_status do
      customer.update_attributes(params[:customer]) &&
      user.update_attributes(params[:user])
    end
  end

end

Profile#update_attributes feels awkward. I realize you're trying to stick with Rail-y looking signatures, but the _attributes suffix is distracting - it has nothing to do with the domain, and is a mere implementation detail of how Profile is "updated."

I think I'd opt to drop the _attributes suffix.

As a side note, in Rails 4, you can use Model#update instead of #update_attributes. Using update here is both more and less Rails-y at the same time :)